Cosmological black holes

The term cosmological black hole for any solution of Einstein equations(Einstein_field_equations) representing a collapsing overdensity region in a cosmological background leading to an infinite density at its center [1]. Older models of black hole are based on the solution of Schwarzschild_metric when Spacetime is asymptotically flat(Asymptotically_flat_spacetime), but if we want to have a more realistic model we need to have an asymptotically FRW spacetime. There have been different attempts to construct solutions of Einstein equations representing such a collapsing central mass. Gluing of a Schwarzschild manifold to an expanding FRW manifold is one of the first attempts to construct such a cosmological black hole, as done first by Einstein and Straus [2]. Models not based on a cut-and-paste technology is much more interesting giving more information on the behavior of the mass condensation within a FRW universe model. The first attempt is due to McVittie [3] introducing a spacetimemetric that represents a point mass embedded in a Friedmann–Robertson–Walker (FRW) universe. There have been many other attempts to construct cosmological black holes [1-3] [4], some of them contrasting some of the features one expect from theory or observation such as non-ordinary matter in energy momentum tensor or strange singularity. More reasonable models are obtained by assuming an ordinary matter in the energy momentum tensor and getting the metric by solving the Einstein equation. This was done for the perfect fluid in the cosmological back ground without any gluing two different manifold [5]. Such cosmological black holes, if based on exact solutions of general relativity and not produced by a cut-and-paste technology, are very interesting laboratories to study not only general relativistic structures, their quasi-local features such as mass and horizons [6]. These cosmological structure models can be regarded as more precise models to verify the astrophysical effect such as gravitational lensing and rotation curve for dark matter [7].

References

[1] Sultana, J., Dyer, C.C.: Gen. Relativ. Gravit. 37, 1349 (2005)

[2] Einstein, A., Straus, E.G.: Rev. Mod. Phys. 17, 120 (1945)
Einstein, A., Straus, E.G.: Rev. Mod. Phys. 18, 148 (1946)

[3] McVittie, G.C.: Mon. Not. R. Astr. Soc. 93, 325 (1933)

[4] Nolan, B.C.: J. Math. Phys. 34, 1 (1993); Faraoni, Valerio and
Jacques, Audrey, Phys.Rev. D76 (2007) 063510;G. W. Gibbons and K. -i.
Maeda, “Black Holes in an Expanding Universe,” Phys. Rev. Lett. 104
(2010) 131101; Marra, Valerio and Paakkonen, Mikko, JCAP 1201 (2012)
025

[5] Firouzjaee, J.T., Mansouri, Reza: Gen. Relativ. Gravit. 10, 2431
(2010); Rahim Moradi, Javad T. Firouzjaee and Reza Mansouri,
[arXiv:1301.1480]

[6] J. T. Firouzjaee, M. Parsi Mood and Reza Mansouri, Gen. Relativ.
Gravit. 44, 639 (2012)

[7] M. Parsi Mood, Javad T. Firouzjaee and Reza Mansouri,
[arXiv:1304.5062]; Mohammadhosein Razbin, J. T. Firouzjaee and Reza
Mansouri [arXiv:1212.4796].